1. Field of the Invention
The invention relates generally to methods for designing the profile of a cam for actuating a valve mechanism. More specifically, the invention relates to generation of an acceleration profile for a valve operating cam of an internal combustion engine, the profile satisfying a plurality of valve motion constraints.
2. Discussion of the Prior Art
Internal combustion engines use a well-known cam shaft system with a plurality of cams for opening and closing various valves associated with individual combustion cylinders of the engine. A conventional cam-actuated engine valve arrangement is shown in FIG. 1. Cam 101 rotates in the direction shown by arrow 113 so as to move cam follower or tappet 103 and push rod 105 against rocker arm 107 which, in turn, causes motion of spring biased valve 111 in an opening or closing direction for controlling communication with cylinder volume 115 with an input or output conduit 113. Valve 111 is biased to a closed or sealed position with respect to conduit 113 by biasing valve spring 109. Zero degree cam angle rotation is defined as when cam nose 101a is in a vertically upward direction as shown in FIG. 1 wherein valve 11 would be in a fully open position.
At the very beginning of the cam design process, a cam designer may be presented with design parameters, such as overlap volume, intake valve closing volume, exhaust pseudo flow velocity and blow down volume. Additionally, manufacturing constraints such as the smallest radius of curvature that can be ground with a specific grinding wheel play a roll in the design process.
Computerized techniques allow designers to specify how the valve is to move by specifying the valve acceleration. These computerized techniques then determine the shape the cam needs to take in order to deliver the desired valve acceleration profile as the cam makes a total rotation.
Unless a design engineer is extremely lucky, the initially selected acceleration profile for the cam will not meet all of a plurality of valve motion constraints without adjusting the initial profile. Prior techniques for transforming draft acceleration curves into an acceleration profile that meets all valve motion constraints are known, wherein a plurality of scaling constants are sought to scale the various acceleration pulses formed by the acceleration curve such that the valve motion constraints will be satisfied. In known systems, there are four valve motion constraints but only three scaling constants due to the nature of the acceleration profile curve. Hence, a fourth design variable is chosen to be an adjustment design point acceleration value of the design engineer's choosing.
The constraint satisfaction problem has conventionally been solved as a non-linear four-dimensional root-finding problem. The adjustment acceleration value and the three scaling constants have in the past been adjusted by generic root-finding software in an effort to determine values of these four design parameters that yield an adjusted trial curve that meets all constraints to within an acceptable error tolerance. There are problems with this known approach. First, sometimes the known approach does not succeed or it does not deliver a highly precise solution. Secondly, this known optimization approach is more computationally expensive than can be tolerated during interactive design within many popular computing environments (e. g., Matlab/Simulink). Hence, a faster approach is needed.